The present invention relates to a method for determining an individual ophthalmic lens adapted to a wearer for whom an astigmatism has been prescribed; such lenses are also called toric ophthalmic lenses; they differ from ophthalmic lenses described as being spherical, the latter being intended to be worn by persons with no prescription for astigmatism. The method can be applied both to single-focus or multifocal lenses.
Multi-focal ophthalmic lenses are well-known; among these multi-focal lenses one can distinguish lenses known as progressive lenses, and lenses that are more specifically dedicated to near vision.
Multi-focal lenses present a particular problem for wearers needing correction of astigmatism. The astigmatism supplied to the wearer is the resultant of three components:
local cylinder of the progressive surface, characterised by its amplitude (or modulus) and its axis;
the prescribed cylinder and its axis;
oblique astigmatism.
Currently, to correct a spectacle wearer suffering from astigmatism, a lens is provided the front face of which is optimized in the case of a spherical prescription, and the rear face of which is a simple torus. Thus, account is not taken of the deterioration introduced by the torus; at best, one can play on the oblique astigmatism by adjusting the base value of the front face. For economic reasons, one cannot multiply the number of basic values existing already.
Multifocal progressive ophthalmic lenses are now well known. They are used for correcting longsightedness and allow the spectacle wearer to view objects over a wide range of distances without needing to take his glasses off. Such lenses typically comprise a far vision region, situated at the top of the lens, a near vision region at the bottom of the lens, the far and near vision regions being joined by an intermediate region, with a main meridian of progression passing through the three regions.
French Patent 2,699,294 describes the different elements of such a progressive multifocal ophthalmic lens in its introductory part, and mentions the works carried out by the applicant to improve the comfort of wearers of such lenses. Reference should be made to that document for more details on these various points.
Applicant has also proposed, for example in U.S. Pat. Nos. 5,270,745 or 5,272,495 to introduce a variation into the meridian, and notably to place it off-center with respect to a near vision control point, as a function of power addition and ametropy.
Applicant has also proposed, in order to better satisfy the visual requirements of presbytic (longsighted) persons and to improve comfort of progressive multifocal lenses, various improvements (French Patents 2,683,642, 2,699,294 and 2,704,327).
Lenses also exist that are more specifically dedicated to near vision; these lenses do not have a far vision region with a defined reference point like one finds in conventional progressive lenses. Such lenses are prescribed as a function of the power the wearer needs for near vision, independently of far vision power. Such a lens is described in an article in the xe2x80x9cOpticien Lunetierxe2x80x9d of April 1988, and is sold by the applicant under the Essilor Delta trademark; this lens is simple to use and just as easy to adapt to as a progressive lens, and is attractive to the population of presbytic persons not fitted with progressive lenses. This lens is also disclosed in French Patent application 2,588,973. It has a central portion which is equivalent to a single-focus lens which one would normally employ for correcting longsightedness, in order to ensure satisfactory near vision. It additionally has a slight decrease in power in the upper portion thereby ensuring the wearer has sharp vision also beyond the usual field of near vision. Finally, the lens has a point, at a value of power equal to the nominal power for near vision, a region of greater power in the lower portion of the lens, and a region of lower power in the upper portion of the lens.
Usually, multifocal lenses, whether they be progressive or dedicated to near vision, have one non-spherical multifocal face, for example the side facing the spectacle wearer, and one spherical or toric face, known as the prescription face. This spherical or toric face allows the lens to be adapted to the users""s ametropy, so that a multifocal lens is generally only defined by its non-spherical surface. As is well known, such a non-spherical surface is generally defined by the altitude of all its points. One also uses parameters constituted by the maximum and minimal curvatures at each point, or more frequently, their half-sum and difference. This half-sum and difference multiplied by a factor nxe2x88x921, n being the refractive index of the material of the lens, are known as mean sphere and cylinder.
For progressive multifocal lenses, one thus defines, by choosing a (power addition, base) pair, a set of non-spherical multifocal faces. Usually, one can thus define 5 basic values and 12 power addition values, giving a total of 60 multifocal faces. In each basic value, an optimization is performed for a given power, i.e. for a spherical prescription face having a given curvature.
The use within one of these multifocal faces of a spherical or toric prescription face having a power close to the prescription face considered for optimization makes it possible to meet all the requirements of wearers of progressive multifocal lenses. This known method makes it possible, starting from semi-finished lenses, of which only the multifocal face has been shaped, to prepare lenses that are adapted to each wearer, by simply machining one spherical or toric prescription face.
A similar method is used for optimization and prescription of lenses dedicated to near vision.
This method has the disadvantage of only being an approximation; consequently, the results obtained with a prescription face that is different from that used for optimization are worse than those corresponding to the prescription face employed for optimization.
U.S. Pat. No. 5,444,503 discloses a lens having a multifocal surface and a prescription surface. Compared to the prior art, which suggests defining the prescription service in order to obtain a given power at the far vision reference point, it is proposed, in that Patent, to define the prescription surface of the lens as a function of the power required by the wearer in a plurality of elementary surfaces. For this, the said United States.
Patent involves calculating aberration over the whole surface, and causing a continuous parametered surface to vary, for example a surface defined by splines, using known mathematical optimization algorithms. In practice, beyond the statement of principle, that Patent proposes using, in order to optimize the prescription surface, the distance to the cornea in an elementary surface, the object distance in an elementary surface, the inclination of the lens in the frame, the shape of the frame, and the curvature of the lens. That Patent says nothing regarding the effective calculation of the prescription surface. According to that document, their solution would make it possible to overcome the defects originating from replacement of the rear face used for optimization, by a rear face close to it.
That solution has the disadvantage of complicating lens manufacture: it involves determining, and machining, a non-spherical rear face. In this case, one should optimise and machine two complex surfaces. The proposed method does not appear to be founded on physiological data.
International application WO-A-96/13748 further discloses the use, for multifocal lenses, of a non-toric prescription surface, in order to limit defects with respect to the prescription surface employed for optimization. That Patent discloses prescription surfaces the main cross sections of which are circles having a radius defined by a given equation, the parameters of the equation depending on the wearer""s sphere and cylinder. The solution disclosed in that document suffers from the same disadvantages as those described with reference to U.S. Pat. No. 5,444,503.
International application WO-A-97/19382 discloses a progressive ophthalmic lens having a front face that is spherical or exhibits symmetry of revolution, and a rear face obtained by combining a progressive surface having a power addition and a toric surface in which the torus is adapted to the wearer""s astigmatism. The formula for combining these two surfaces is stated in the Patent, and gives the altitude of a point as a function of its coordinates in an orthonormalized reference frame, of mean sphere of the progressive surface at this point, and of curves for the progressive surface in the directions of the orthonormalized reference frame.
The algebraic combination of the two surfaces in that patent, using the given formula for combination, does not give satisfactory optical results. This method obliges the manufacturer to re-incline the front surface of the lens to obtain a satisfactory optical quality, thereby deteriorating lens aesthetics.
The prior art Patents say little or are not explicit regarding calculation techniques. Their techniques do not appear to be founded on physiological data, and do not use ray tracing.
The invention provides a method for determining a toric lens, based on a physiological law, making it possible to take account of the torsion of the eye for any given direction of glance. For each direction of glance, it is arranged for power and astigmatism, both as regards their value and direction, to be as close as possible to the prescription in the reference frame associated with the eye. Calculation of astigmatism in this reference frame makes it possible to take account of the effect of torsion of the eye, when the spectacle wearer is looking in an off-center direction. The method employs ray tracing and consequently an optical method.
The invention discloses a method making it possible to define a lens adapted for a toric prescription, the target being the behavior of a spherical lens; in this context, we shall call a spherical lens a lens that is adapted to be prescribed for a non-astigmatic wearer; i.e. not having overall cylinder.
The invention thus makes it possible to obtain lenses that are suitable for astigmatic spectacle wearers, which have better optical characteristics than those of the prior art.
The general method disclosed, which can be applied to any type of lens, makes it possible to overcome the disadvantages due to torus in a conventional toric prescription, and to give the spectacle wearer a perception which is equivalent to that of a spherical prescription.
The invention also provides for calculation of a lens that is unique for each prescription. Using other parameters, such as the shape of the frame, the distance between the cornea and the lens, the pantoscopic angle, it is possible to calculate a lens for each wearer.
More precisely, the invention discloses a method for the determination, using optimization, of an ophthtalmic lens for a wearer for whom an astigmatism has been prescribed, comprising the steps of:
selecting a starting lens and defining a working lens to be equal to the starting lens; selecting a target lens;
modifying the working lens, in order to minimize, in a plurality of directions of glance and in a reference frame associated with the eye:
a difference between power of said working lens and power of the said target lens;
a difference between residual astigmatism and astigmatism of the target lens;
residual astigmatism being defined as the difference between an astigmatism prescribed and astigmatism generated by the working lens both as regards amplitude and the axis thereof in the reference frame associated with the eye, and for each direction of glance.
Advantageously, power, astigmatism and residual astigmatism are calculated by ray tracing.
In a preferred embodiment, prescribed astigmatism is represented by expansion (A3, A4, A5) thereof into Zernike polynomials, and in which, in each direction of glance, the wave surface generated by the working lens is represented by the expansion (axe2x80x23, axe2x80x24,axe2x80x25) thereof into Zernike polynomials, and wherein amplitude of residual astigmatism in said direction of glance is equal to
4{square root over ((axe2x80x23xe2x88x92A3+L ) 2+L +(axe2x80x25xe2x88x92A5+L )2+L )}.
In another embodiment, in each direction of glance, a wave surface generated by said working lens is represented by expansion (axe2x80x23, axe2x80x24, axe2x80x25) thereof into Zernike polynomials, and power in said direction of glance is equal to 4axe2x80x24.
Preferably, the ophthalmic lens is a progressive lens.
In one embodiment, the ophthalmic lens is a lens dedicated to near vision.
Advantageously, orientation of the reference frame associated with the eye in a direction of glance (xcex1, xcex2) is deduced from orientation of the reference frame in the direction (axe2x80x23, axe2x80x24, axe2x80x25)xcex1=xcex2=0 by means of Listing""s law.
Preferably, the said target lens is a spherical lens.
In one embodiment, the step of modifying the working lens is iterated in order to cause said differences to decrease.
In another embodiment, the step of modifying the working lens comprises modifying one single surface thereof.
A lens obtained by the above method, the surface of which is toric or spherical, is also provided.
Other advantages and characteristics of the invention will become more clear from the description which follows of several embodiments, provided by way of example and with reference to the attached drawings.